JEE Main & Advanced Mathematics Functions Question Bank Self Evaluation Test - Relations and Functions-I

If a function F is such that \[F(0)=2,F(1)=3,\]\[F(x+2)=2F(x)-F(x+1)\] for \[x\ge 0,\] then \[F(5)\] is equal to

A) -7

B) -3

C) 17

D) 13

Correct Answer: D

Solution :

[d] We have, \[F(x+2)=2F(x)-F(x+1)...\] (i)

\[x=0\,\,in\,\,(1)\Rightarrow F(2)=2F(0)-F(1)=2(2)-3=1\]

\[x=1\,\,in\,\,(1)\Rightarrow F(3)=2F(1)-F(2)=2(3)-1=5\]

\[x=2\,\,in\,(1)\Rightarrow F(4)=2F(2)-F(3)=2(1)-5=-3\]

\[x=3\,\,in\,\,(1)\Rightarrow F(5)=2F(3)-F(4)=2(5)-(-3)=13\]\[\therefore \] The correct answer is (d).